On Fourier Transforms of Radial Functions and Distributions

被引：41

作者：

Grafakos, Loukas ^{[1
]}

Teschl, Gerald ^{[2
,3
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[3] Int Erwin Schrodinger Inst Math Phys, A-1090 Vienna, Austria

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2013年 / 19卷 / 01期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

Radial Fourier transform; Hankel transform;

D O I：

10.1007/s00041-012-9242-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find a formula that relates the Fourier transform of a radial function on R (n) with the Fourier transform of the same function defined on R (n+2). This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t bar right arrow f(|t|) and the two-dimensional function (x (1),x (2)) bar right arrow f(|(x (1),x (2))|). We prove analogous results for radial tempered distributions.

引用

页码：167 / 179

页数：13

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